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  "body": "\n## Description\n\nThe Euler–Mascheroni constant is the real number\n$$\\gamma = \\lim_{n \\to \\infty} \\big( H_n - \\ln n \\big) \\approx 0.5772156649,$$\nwhere $H_n = 1 + \\frac{1}{2} + \\cdots + \\frac{1}{n}$ is the $n$-th [[harmonic number|0D2Y6G4C4S]].\n\n## Remarks\n\nThe [[limit exists|05S2GSPMGA]], because the sequence $H_n - \\ln n$ is decreasing and bounded below by $0$.\nAlso $\\gamma = \\int_1^\\infty \\Big( \\frac{1}{\\lfloor x \\rfloor} - \\frac{1}{x} \\Big) \\, dx$.\nIt is not known whether $\\gamma$ is rational. Mathlib defines it as `Real.eulerMascheroniConstant`.\nLeonhard Euler introduced the constant in a paper of 1734. Lorenzo Mascheroni later computed it to more decimal places, with some errors.\n\n## Explanations\n\n### L1 human\n\nThe harmonic numbers grow like $\\ln n$, and $\\gamma$ is the limit of the difference.\nSo $H_n \\approx \\ln n + 0.5772$ for large $n$.\n",
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